---
_id: '30790'
abstract:
- lang: eng
  text: "Iterative distributed optimization algorithms involve multiple agents that\r\ncommunicate
    with each other, over time, in order to minimize/maximize a global\r\nobjective.
    In the presence of unreliable communication networks, the\r\nAge-of-Information
    (AoI), which measures the freshness of data received, may be\r\nlarge and hence
    hinder algorithmic convergence. In this paper, we study the\r\nconvergence of
    general distributed gradient-based optimization algorithms in\r\nthe presence
    of communication that neither happens periodically nor at\r\nstochastically independent
    points in time. We show that convergence is\r\nguaranteed provided the random
    variables associated with the AoI processes are\r\nstochastically dominated by
    a random variable with finite first moment. This\r\nimproves on previous requirements
    of boundedness of more than the first moment.\r\nWe then introduce stochastically
    strongly connected (SSC) networks, a new\r\nstochastic form of strong connectedness
    for time-varying networks. We show: If\r\nfor any $p \\ge0$ the processes that
    describe the success of communication\r\nbetween agents in a SSC network are $\\alpha$-mixing
    with $n^{p-1}\\alpha(n)$\r\nsummable, then the associated AoI processes are stochastically
    dominated by a\r\nrandom variable with finite $p$-th moment. In combination with
    our first\r\ncontribution, this implies that distributed stochastic gradient descend\r\nconverges
    in the presence of AoI, if $\\alpha(n)$ is summable."
author:
- first_name: Adrian
  full_name: Redder, Adrian
  id: '52265'
  last_name: Redder
  orcid: https://orcid.org/0000-0001-7391-4688
- first_name: Arunselvan
  full_name: Ramaswamy, Arunselvan
  id: '66937'
  last_name: Ramaswamy
  orcid: https://orcid.org/ 0000-0001-7547-8111
- first_name: Holger
  full_name: Karl, Holger
  id: '126'
  last_name: Karl
citation:
  ama: Redder A, Ramaswamy A, Karl H. Distributed gradient-based optimization in the
    presence of dependent  aperiodic communication. <i>arXiv:220111343</i>. Published
    online 2022.
  apa: Redder, A., Ramaswamy, A., &#38; Karl, H. (2022). Distributed gradient-based
    optimization in the presence of dependent  aperiodic communication. In <i>arXiv:2201.11343</i>.
  bibtex: '@article{Redder_Ramaswamy_Karl_2022, title={Distributed gradient-based
    optimization in the presence of dependent  aperiodic communication}, journal={arXiv:2201.11343},
    author={Redder, Adrian and Ramaswamy, Arunselvan and Karl, Holger}, year={2022}
    }'
  chicago: Redder, Adrian, Arunselvan Ramaswamy, and Holger Karl. “Distributed Gradient-Based
    Optimization in the Presence of Dependent  Aperiodic Communication.” <i>ArXiv:2201.11343</i>,
    2022.
  ieee: A. Redder, A. Ramaswamy, and H. Karl, “Distributed gradient-based optimization
    in the presence of dependent  aperiodic communication,” <i>arXiv:2201.11343</i>.
    2022.
  mla: Redder, Adrian, et al. “Distributed Gradient-Based Optimization in the Presence
    of Dependent  Aperiodic Communication.” <i>ArXiv:2201.11343</i>, 2022.
  short: A. Redder, A. Ramaswamy, H. Karl, ArXiv:2201.11343 (2022).
date_created: 2022-04-06T06:53:38Z
date_updated: 2022-11-18T09:33:01Z
department:
- _id: '75'
external_id:
  arxiv:
  - '2201.11343'
language:
- iso: eng
project:
- _id: '16'
  name: 'SFB 901 - C4: SFB 901 - Subproject C4'
- _id: '1'
  name: 'SFB 901: SFB 901'
- _id: '4'
  name: 'SFB 901 - C: SFB 901 - Project Area C'
publication: arXiv:2201.11343
status: public
title: Distributed gradient-based optimization in the presence of dependent  aperiodic
  communication
type: preprint
user_id: '477'
year: '2022'
...